KEPLER Exoplanets Database

Observed exoplanet's periods VS. theoretical period calculated with stimated star mass and exoplanet mass.

Source: https://data.world/markmarkoh/kepler-confirmed-planets/workspace/project-summary?agentid=markmarkoh&datasetid=kepler-confirmed-planets NASA Exoplanet archive: https://exoplanetarchive.ipac.caltech.edu/docs/data.html

@Author: Javier Cebriรกn

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Correlation Obital Period [days] & Orbit Semi-Major Axis [AU]

Orbit Period and Semi-major Axis is related with the following equation:

image.png

Where a=semi-major axis , T=period and ฮผ=MG with M=Mass of star and G=Gravity cte

$ T โˆ a^{3/2} $

Whith scatter representacion can be observed that correlation value is affected by Oph 11 exoplanet outlier.

Oph 11 is an outlier

Error theory aproximation for planets with stars of known mass:

Applying the theory described at the beginning here is calculated the approximate result of the extrasolar planet's orbital period.

$ T \approx \sqrt{\frac{a^3}{ \frac{GM}{4 \pi^2}}}\ $

With a=semi-major axis , M=Mass of star and G=Gravity

a = 'pl_orbsmax' is the semi-major axis.

M = 'st_mass' is the mass star in solar masses.

4434075.792 is a factor to use solar masses and UA units

Mean squared error:

More exactly:

$ T = \sqrt{\frac{a^3}{ \frac{G(M+m)}{4 \pi^2}}}\ $

With a=semi-major axis , M=Mass of star, m=mass of the planet and G=Gravity

a = 'pl_orbsmax' is the semi-major axis.

M = 'st_mass' is the mass star in solar masses.

4434075.792 is a factor to use solar masses and UA units

m = 'pl_bmassj' is the planet mass in Jupiter masses (Jupiter has $9.55ยท10^{-4}$ solar masses)

Mean squared error:

Conclusion:

Correlation shows relation between observed period and orbital axis. The observations conform to the theoretical calculation:

$ T = \sqrt{\frac{a^3}{ \frac{G(M+m)}{4 \pi^2}}}\ $

With a=semi-major axis , M=Mass of star, m=mass of the planet and G=Gravity

The relation measured is causal.